57
Views
10
CrossRef citations to date
0
Altmetric
Miscellany

Optimization of approximating networks for optimal fault diagnosis

&
Pages 241-266 | Received 31 Jul 2003, Accepted 28 Oct 2003, Published online: 31 Jan 2007

References

References

  • Gertler , JJ . 1988 . Survey of model-based failure detection and isolation in complex plants . IEEE Control Systems Magazine , 8 ( 6 ) : 3 – 11 .
  • Frank , PM . 1990 . Fault diagnosis in dynamic system using analytical and knowledge-based redundancy. A survey and some new results . Automatica , 26 ( 3 ) : 459 – 474 .
  • Zhang , X , Polycarpou , MM and Parisini , T . 2001 . Robust fault isolation of a class of nonlinear input-output systems . International Journal of Control , 74 ( 133 ) : 1295 – 1310 .
  • Zhang , X , Polycarpou , MM and Parisini , T . 2002 . A robust detection and isolation scheme for abrupt and incipient faults in nonlinear systems . IEEE Transactions on Automatic Control , 47 ( 4 ) : 576 – 593 .
  • Alcorta-Garcia , E and Frank , PM . 1997 . Deterministic nonlinear observer-based approaches to fault diagnosis: A survey . Control Engineering Practice , 5 ( 5 ) : 663 – 670 .
  • De Persis , C and Isidori , A . 2001 . A geometric approach to nonlinear fault detection and isolation . IEEE Transactions on Automatic Control , 46 ( 6 ) : 853 – 865 .
  • Massoumnia , MA . 1986 . A geometric approach to the synthesis of failure detection filters . IEEE Transactions on Automatic Control , 31 ( 9 ) : 839 – 846 .
  • Duyar , A , Eldem , V , Merril , W and Guo , T . 1994 . Fault detection and diagnosis in propulsion systems: A fault parameter estimation approach . Journal of Guidance, Control, and Dynamics , 17 ( 1 ) : 104 – 108 .
  • Niedźwiecki , M . 1994 . Identification of time-varying systems with abrupt parameter changes . Automatica , 30 ( 3 ) : 447 – 459 .
  • Girosi , F . 1998 . An equivalence between sparse approximation and support vector machines . Neural Computation , 10 ( 6 ) : 1455 – 1480 .
  • Zoppoli R Parisini T 1992 Learning techniques and neural networks for the solution of N-stage nonlinear nonquadratic optimal control problems In: A. Isidori and T.J. Tarn, (Eds) Systems, Models and Feedback: Theory and Applications Boston Birkhauser
  • Parisini , T and Zoppoli , R . 1996 . Neural approximation for multistage optimal control of nonlinear stochastic systems . IEEE Transactions on Automatic Control , 41 ( 6 ) : 889 – 895 .
  • Parisini , T and Zoppoli , R . 1994 . Neural networks for feedback feedforward nonlinear control systems . IEEE Transactions on Neural Networks , 5 ( 3 ) : 436 – 449 .
  • Zoppoli , R , Sanguineti , M and Parisini , T . 2002 . Approximating networks and the extended Ritz method for the solution of functional optimization problems . Journal of Optimization Theory and Applications , 112 ( 2 ) : 403 – 439 .
  • Baglietto , M , Parisini , T and Zoppoli , R . 2001 . Numerical solutions to the Witsenhausen counterexample by approximating networks . IEEE Transactions on Automatic Control , 46 ( 9 ) : 1471 – 1477 .
  • Kůrková V Sanguineti M 2002 Error estimates for approximate solution of optimization problems by neural networks In: Workshop on Mathematical Diagnostics, Book of Abstracts pp. 11–12 See also: Kůrková, V. and Sanguineti, M., 2002, Error estimates for approximate optimization over variable-basis functions. Research Report ICS-2002-882, Institute of Computer Science, Prague (submitted)
  • Kainen , PC , Kůrková , V and Sanguineti , M . 2003 . Minimization of error functionals over variable-basis functions . SIAM Journal on Optimization , 14 ( 3 ) : 732 – 742 .
  • Baglietto , M , Parisini , T and Zoppoli , R . 2001 . Distributed-information neural control: The case of dynamic routing in traffic networks . IEEE Transactions on Neural Networks , 12 ( 3 ) : 485 – 502 .
  • Baglietto M Sanguineti M Zoppoli R 2003 Facing the curse of dimensionality by the extended Ritz method in stochastic functional optimization: Dynamic routing in traffic networks In: G. Di Pillo and A. Murli (Eds) Applied Optimization Dordrecht The Netherlands Kluwer Academic Publishers pp. 23–56
  • Bellman R 1957 Dynamic Programming Princeton NJ Princeton University Press
  • Beard , RW and McLain , TW . 1998 . Successive Galerkin approximation algorithms for nonlinear optimal and robust control . International Journal of Control , 71 ( 5 ) : 717 – 743 .
  • Barron , AR . 1993 . Universal approximation bounds for superpositions of a sigmoidal function . IEEE Transactions on Information Theory , 39 ( 3 ) : 930 – 945 .
  • Breiman , L . 1993 . Hinging hyperplanes for regression, classification, and function approximation . IEEE Transactions on Information Theory , 39 ( 3 ) : 993 – 1013 .
  • Kůrková , V and Sanguineti , M . 2001 . Bounds on rates of variable-basis and neural-network approximation . IEEE Transactions on Information Theory , 47 ( 6 ) : 2659 – 2665 .
  • Kůrková , V and Sanguineti , M . 2002 . Comparison of worst-case errors in linear and neural network approximation . IEEE Transactions on Information Theory , 48 ( 1 ) : 264 – 275 .
  • Chen , VCP , Ruppert , D and Shoemaker , CA . 1999 . Applying experimental design and regression splines to high-dimensional continuous-state stochastic dynamic programming . Operations Research , 47 : 38 – 53 .
  • Johnson , SA , Stedinger , JR , Shoemaker , C , Li , Y and Tejada-Guibert , J . 1993 . Numerical solution of continuous-state dynamic programs using linear and spline interpolation . Operations Research , 41 : 484 – 500 .
  • Alessandri , A , Parisini , T and Zoppoli , R . 1997 . Neural approximators for nonlinear finite-memory state estimation . International Journal of Control , 67 ( 2 ) : 275 – 302 .
  • Sjöberg , J , Zhang , Q , Ljung , L , Benveniste , A , Glorennec , P-Y , Delyon , B , Hjalmarsson , H and Juditsky , A . 1995 . Nonlinear black-box modeling in system identification: A unified overview . Automatica , 31 : 1691 – 1724 .
  • Giulini , S and Sanguineti , M . 2000 . On dimension-independent approximation by neural networks and linear approximators . Proceedings of International Joint Conference on Neural Networks , 1 : 1283 – 1288 .
  • Kushner HJ Yin GG 1997 Stochastic Approximation Algorithms and Applications New York Springer Verlag
  • Srinivasan , B , Prasad , UR and Rao , NJ . 1994 . Backpropagation through adjoints for the identification of nonlinear dynamic systems using recurrent neural models . IEEE Transactions on Neural Networks , 5 ( 2 ) : 213 – 228 .
  • Rumelhart DE Hinton GE Williams RJ 1986 Learning internal representation by error propagation, In: D.E. Rumelhart, J.L. McClelland and the PDP Research Group (Eds) Parallel Distributed Processing: Explorations in the Microstructures of Cognition Cambridge MA MIT
  • Gelb A 1974 Applied Optimal Estimation Reading MA MIT Press
  • Zhang , Q , Basseville , M and Benveniste , A . 1994 . Early warning of slight changes in systems . Automatica , 30 ( 1 ) : 95 – 113 .
  • Parthasarathy T 1983 On Global Univalence Theorems, Lecture Notes in Mathematics Berlin Springer Verlag
  • Rudin W 1976 Principles of Mathematical Analysis Singapore McGraw-Hill

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.